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Math Help - Logics exercise - Must be pretty easy for mathematicians

  1. #1
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    Logics exercises (should be a cake walk for mathematicians)

    Hey, I was once challenged to find the answers to two exercises, on which I had success, but only by the means of trial and error.
    Could somebody show me the heuristics to solve them? The exercises are as follows:

    EXERCISE 1

    There are three balls, labeled A, B and C.One of them is blue, other is white, and the last one is red. Only one of the following propositions is right:

    - A is red
    - B is not red
    - C is not blue

    Which are the colors for A, B and C?

    EXERCISE 2

    Adrian, Bob and Carl all work at the same firm. One of them is a director, other is a secretary, and the last one is a janitor. Bob is the only one who is known for always telling the truth.

    -The director said Bob is a secretary
    -The secretary said his name is Bob
    -The janitor said Adrian is a director.

    Which are the positions of Adrian, Bob and Carl in the firm?
    Last edited by Schiavo; June 29th 2013 at 07:16 PM.
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  2. #2
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    Re: Logics exercise - Must be pretty easy for mathematicians

    Logic is a great topic.

    For exercise 1:
    We handle the 3 cases individually. Let's start with A is red being the only thing true. That means the other two statements are not true, so B is not not red, hence B is also red, and that is impossible. So we look at the next possibility of B is not red being true. Since A is red must be false then, C must be red, but that is impossible since then C is not blue would be true, making two statements true. Therefore, B is not red is not true. That leaves us with C is not blue being the true phrase. That means that B is red, A is blue and C is white.'


    Exercise 2:

    I am unsure about this exercise as numerous situations are possible because people besides Bob can both lie and tell the truth,unless you meant that only Bob tells the truth. When you said Bob is the only one who is known for ALWAYS telling the truth, that means that the others could potentially tell the truth, but they also lie. With this fact, Bob = secretary Carl = director Adrian = janitor, Bob=secretary Carl = janitor, Adrian = director, Bob = janitor Adrian = director Carl = secretary, these situations are all possible. If only Bob can tell the truth, then the only possibility is Bob = janitor Adrian = director Carl = secretary.
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  3. #3
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    Re: Logics exercise - Must be pretty easy for mathematicians

    Hey Schiavo.

    Can you show us your attempts please?
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